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However, this formal similarity notwithstanding, possessing a complex-antiderivative is a much more restrictive condition than its real counterpart. While it is possible for a discontinuous real function to have an anti-derivative, anti-derivatives can fail to exist even for holomorphic functions of a complex variable.
In graph theory, a part of discrete mathematics, the BEST theorem gives a product formula for the number of Eulerian circuits in directed (oriented) graphs. The name is an acronym of the names of people who discovered it: N. G. de Bruijn , Tatyana Ehrenfest , Cedric Smith and W. T. Tutte .
The slope field of () = +, showing three of the infinitely many solutions that can be produced by varying the arbitrary constant c.. In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral [Note 1] of a continuous function f is a differentiable function F whose derivative is equal to the original function f.
The Andrásfai graph And(n) for any natural number n ≥ 1 is a circulant graph on 3n – 1 vertices, in which vertex k is connected by an edge to vertices k ± j, for every j that is congruent to 1 mod 3. For instance, the Wagner graph is an Andrásfai graph, the graph And(3). The graph family is triangle-free, and And(n) has an independence ...
Curve fitting [1] [2] is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, [3] possibly subject to constraints. [ 4 ] [ 5 ] Curve fitting can involve either interpolation , [ 6 ] [ 7 ] where an exact fit to the data is required, or smoothing , [ 8 ] [ 9 ] in which a "smooth ...
His second proof was geometric. If () = and () =, the theorem can be written: + =.The figure on the right is a proof without words of this formula. Laisant does not discuss the hypotheses necessary to make this proof rigorous, but this can be proved if is just assumed to be strictly monotone (but not necessarily continuous, let alone differentiable).
Simplex vertices are ordered by their values, with 1 having the lowest (() best) value. Mathematical optimization (alternatively spelled optimisation ) or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives.
In graph theory, the blossom algorithm is an algorithm for constructing maximum matchings on graphs. The algorithm was developed by Jack Edmonds in 1961, [1] and published in 1965. [2] Given a general graph G = (V, E), the algorithm finds a matching M such that each vertex in V is incident with at most one edge in M and | M | is maximized. The ...